Given the narratives about the cold war I can forgive you for saying that but no. One side using a proxy to attack the other side is still IMO a proxy war. They're waging war but via their proxy. I don't think it's requisite for both sides to use a proxy, just one. (Take Vietnam for example, US accused Vietnam of being a Soviet proxy, attacked it directly after its own proxy started losing. Obviously Vietnam was not a Soviet proxy, the US just saw beating on them as a way to attack the Soviets via proxy. Same with Korea.)